Thread: Two very irritating area problems. (polar, and restricted area)

hi guys

1. A curve is given in polar coordinates of r = cos ^ 2 fi , 0 <= fi <= 2 pi
How big area does the place/area have which is enclosed by the curve?.


2. calculate the area of the restricted area which is located between the curves y = x^3 and y = x^4.

Ok as far as I am concerned you don't necesserily need to draw this in x and y axis do I? the thing is how to get to know the limits of integration analytically ? I am very bad at finding stuff like this in graphical solutions

Originally Posted by reaz

hi guys

1. A curve is given in polar coordinates of
How big area does the place/area have which is enclosed by the curve?.

That is 'phi'(the Greek letter). Not 'fi', as in "fee-fi-fo-fum, I smell the blood of an....".

Wait, before I finish that, you aren't an Englishman, are you?.

Anyway, Just use the polar integration thingy.

Originally Posted by reaz

hi guys

1. A curve is given in polar coordinates of r = cos ^ 2 fi , 0 <= fi <= 2 pi
How big area does the place/area have which is enclosed by the curve?.


2. calculate the area of the restricted area which is located between the curves y = x^3 and y = x^4.

Ok as far as I am concerned you don't necesserily need to draw this in x and y axis do I? the thing is how to get to know the limits of integration analytically ? I am very bad at finding stuff like this in graphical solutions

For the second question,



Where the dx domain comes from equating

These are equal at 0 and 1. But notice on the interval that

So our dy domain is from to

... Englishman, Be he alive, or be he dead. I'll have his bones to grind my bread ^^


Anyway thanks for the hints I will try to proceed from what's been given by u guys.